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3 years ago

Which of the following expressions is written in scientific notation? 0.2 × 10^-5 31.4 × 10^4 13 × 10^4 1 × 10^-3

Mathematics

2 answers:

saul85 [17]3 years ago

7 0

Answer:

0.2 × 10^-5 31.4

Step-by-step explanation:

fredd [130]3 years ago

4 0

I got 0.2 x 10-5 31.4

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What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

Serggg [28]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-2\\
n=6\\
S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
\\\\\\
-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
\\\\\\
\cfrac{-105}{-21}=a_1\implies 5=a_1$

7 0

3 years ago

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

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3 years ago

Melissa has more than 40 coins in her collection which inequality the nuber of coinsin melissas collection

nata0808 [166]

Answer:

X > 40

Step-by-step explanation:

Given that:

Let number of coins in her collection is more Than 40

To represent the number of coins in Melissa's collection as an inequality :

Let total number of items in her collection = X

Coins in her collection > 40

Hence, coins in her collection can be represented as :

X > 40

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3 years ago

Snack in our class occurs at 9:50 am. We eat lunch at 12:05 pm. How long to students need to wait

Novay_Z [31]

Answer:

2 hours and 15 minutes

Step-by-step explanation:

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3 years ago

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There are 4 granola bars. Three friends want to share them evenly.

melomori [17]

Answer:

4/3 or 1 and 1/3 or 1.33333 repeating

Step-by-step explanation:

you have 4 granola bars and 3 friends and you want to divide them among 3 friends

4/3

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3 years ago

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